Nonbacktracking Spectral Clustering of Nonuniform Hypergraphs

Spectral methods offer a tractable, global framework for clustering in graphs via eigenvector computations on graph matrices. Hypergraph data, which entities interact edges of arbitrary size, poses challenges matrix representations and therefore spectral clustering. We study nonuniform hypergraphs based the hypergraph nonbacktracking operator. After reviewing definition this operator its basic properties, we prove theorem Ihara–Bass type allows eigenpair to take place smaller matrix, often enabling faster computation. then propose an alternating algorithm inference stochastic blockmodel linearized belief-propagation involves step again using operators. provide proofs related that both formalize extend several previous results. pose conjectures about limits detectability blockmodels general, supporting these with in-expectation analysis eigenpairs our perform experiments real synthetic data demonstrate benefits over graph-based ones when interactions different sizes carry information cluster structure.